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Geometria2D`Conicas`
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In the command below, type the new coordinates of the points. You can also change the extension to X and Y. Evaluate the notebook.
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BrocardInellipse[tri={{-5,5},{6,12},{9,-4}},{-15,15},{-15,15}]
Brocard's inellipse equation is:
-287.274+102.959x-18.625
2
x
+191.989y+xy-19.3231
2
y
= 0
The values of a, b, c,
LL´
and e are:
4.34109
4.20376
1.0833
8.14152
0.249546
Major axis in x''
After the rotation the equation is:
1.
´
x
+0.681007
´
y
1.59539+0.101987
´2
x
+0.10876
´2
y
The rotation angle is:
θ = 27.5413°
After the translation the equation is:
1.
´´2
x
+1.06641
´´2
y
18.8451
The coordinates of the new origin are:
´´
O
​(4.90259,3.13079)
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Brocard's inellipse and center
Symmedians and their intersection points with each side of the triangle
Lemoine point
Points obtained with the center of the inellipse and the intersection points of the symmedians, using property of the midpoint on the diameter.